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Proving Triangles Congruent

Proving Triangles Congruent. F. B. A. C. E. D. The Idea of a Congruence. Two geometric figures with exactly the same size and shape. How much do you need to know. . . . . . about two triangles to prove that they are congruent?.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent www.assignmentpoint.com

  2. F B A C E D The Idea of a Congruence Two geometric figures with exactly the same size and shape. www.assignmentpoint.com

  3. How much do you need to know. . . . . . about two triangles to prove that they are congruent? www.assignmentpoint.com

  4. Corresponding Parts • AB DE • BC EF • AC DF •  A  D •  B  E •  C  F B A C E F D In Lesson 4.2, you learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. ABC DEF www.assignmentpoint.com

  5. SSS SAS ASA AAS Do you need all six ? NO ! www.assignmentpoint.com

  6. Side-Side-Side (SSS) E B F A D C • AB DE • BC EF • AC DF ABC DEF www.assignmentpoint.com

  7. Side-Angle-Side (SAS) B E F A C D • AB DE • A D • AC DF ABC DEF included angle www.assignmentpoint.com

  8. Included Angle The angle between two sides H G I www.assignmentpoint.com

  9. E Y S Included Angle Name the included angle: YE and ES ES and YS YS and YE E S Y www.assignmentpoint.com

  10. Angle-Side-Angle (ASA) B E F A C D • A D • AB  DE • B E ABC DEF included side www.assignmentpoint.com

  11. Included Side The side between two angles GI GH HI www.assignmentpoint.com

  12. E Y S Included Side Name the included angle: Y and E E and S S and Y YE ES SY www.assignmentpoint.com

  13. Angle-Angle-Side (AAS) B E F A C D • A D • B E • BC  EF ABC DEF Non-included side www.assignmentpoint.com

  14. Warning: No SSA Postulate There is no such thing as an SSA postulate! E B F A C D NOT CONGRUENT www.assignmentpoint.com

  15. Warning: No AAA Postulate There is no such thing as an AAA postulate! E B A C F D NOT CONGRUENT www.assignmentpoint.com

  16. SSS correspondence • ASA correspondence • SAS correspondence • AAS correspondence • SSA correspondence • AAA correspondence The Congruence Postulates www.assignmentpoint.com

  17. Name That Postulate (when possible) SAS ASA SSA SSS www.assignmentpoint.com

  18. Name That Postulate (when possible) AAA ASA SSA SAS www.assignmentpoint.com

  19. Name That Postulate (when possible) Vertical Angles Reflexive Property SAS SAS Reflexive Property Vertical Angles SSA SAS www.assignmentpoint.com

  20. HW: Name That Postulate (when possible) www.assignmentpoint.com

  21. HW: Name That Postulate (when possible) www.assignmentpoint.com

  22. Let’s Practice ACFE Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: B D For SAS: AF For AAS: www.assignmentpoint.com

  23. HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS: www.assignmentpoint.com

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